function result = miecoated_S12(m1, m2, x, y, u)

  % Coated-sphere Mie-Scattering functions S1 and S2
  % for complex refractive index ratios m1,2=m1,2'+im1,2",
  % size parameters x=k0*a, y=k0*b, and u=cos(scattering angle),
  % where k0=vacuum wave number, a=sphere radius;
  % s. p. 111-114, Bohren and Huffman (1983) BEWI:TDD122
  % C. M�tzler, July 2002

  nmax = round(2 + y + 4 * y^(1/3));
  abcd = miecoated_ab1(m1, m2, x, y);
  an = abcd(1, :);
  bn = abcd(2, :);

  pt = mie_pt(u, nmax);
  pin = pt(1, :);
  tin = pt(2, :);

  n = (1:nmax);
  n2 = (2 * n + 1) ./ (n .* (n + 1));
  pin = n2 .* pin;
  tin = n2 .* tin;
  S1 = (an * pin' + bn * tin');
  S2 = (an * tin' + bn * pin');

  result = [S1; S2];
